Answer:
The test contains 10 three-point questions and 14 five-point questions
Step-by-step explanation:
Given equations are:
[tex]x+y = 24\\and\\3x+5y=100[/tex]
From 2nd equation we can deduce that x represents number of 3-point questions and y represents number of 5-point questions.
Using the substitution method:
From x+y = 24
y= 24-x
Putting this valu of y in 3x+5y=100
[tex]3x+5(24-x) = 100\\3x + 120 - 5x = 100\\-2x+120=100\\-2x = 100-120\\-2x = -20\\\frac{-2x}{-2} = \frac{-20}{-2}\\ x = 10\\Putting\ the\ value\ of\ x\ in\ x+y=24\\10+y=24\\y = 24-10\\y = 14[/tex]
Hence, the correct answer is:
The test contains 10 three-point questions and 14 five-point questions..
The mass of a marine organism, in pounds, p years after it is born is given by the polynomial function R(p)=−4p2+300p. Find the mass when p=20 years .
Answer:
R(p) = -4p^2 + 300p when p=20.
R(p) = -4(20)^2 + 300(20)
R(p) = -1600 + 6000
R(p) = 4400
The mass when p=20 years is 4400.
y = x^2+ 7x - 5 can be written in the form y = (x + a)^2+b
Find the value of a and the value of b
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = (x - h)² + k (h, k) are the coordinates of the vertex
Given y = x² + 7x - 5
To express in vertex form use the method of completing the square
add/subtract ( half the coefficient of the x- term )²
y = x² + 2( [tex]\frac{7}{2}[/tex] )x +[tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] - 5
y = (x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] - [tex]\frac{20}{4}[/tex]
y = (x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{69}{4}[/tex]
Hence
a = [tex]\frac{7}{2}[/tex] and b = - [tex]\frac{69}{4}[/tex]
Which is the simplified form of the expression?
Answer:
Step-by-step explanation:
a
Answer:
4/x14y8 - Last Option
multiply the polynomial (2x^2+5x+5)(4x-3)
So I simplify the expression and it is..
8x^3 + 14x^2 + 5x − 15
____
I hope this helps, as always. I wish you the best of luck and have a nice day, friend..
Find the equation of the line that passes through the pair of points.
(1,5), (1, - 3)
Answer:
x = 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (1, 5) and (1, -3).
Substitute:
[tex]m=\dfrav{-3-5}{1-1}=\dfrac{-8}{0}\ \bold{!}[/tex]
Dividing by zero is not possible.
The slope does not exist.
Conclusion: this is a vertical line with the equation x = a
From the points
(1, 5) → x = 1, y = 5
(1, -3) → x = 1, y = -3
we have the equation x = 1.
What is the length of AC? Round to the nearest tenth.
Answer:
AC ≈ 10.5 cm (1 dec. place )
Step-by-step explanation:
Given
tan55° = [tex]\frac{15}{b}[/tex]
Multiply both sides by b
b × tan55° = 15 ( divide both sides by tan55° )
AC = b = [tex]\frac{15}{tan55}[/tex] ≈ 10.5 cm
Which expression is equivalent to -2 1/4÷ (-2/3)
Answer:
[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)=\dfrac{27}{8}=3\dfrac{3}{8}}[/tex]
Step-by-step explanation:
[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)\qquad\text{the quotient of two negative numbers is positive}\\\\=2\dfrac{1}{4}\div\dfrac{2}{3}\qquad\text{convert the mixed number to the improper fraction}\\\\=\dfrac{2\cdot4+1}{4}\div\dfrac{2}{3}=\dfrac{9}{4}\div\dfrac{2}{3}\\\\\text{dividing by a fraction is the same as multiplying by its reciprocal.}\\\\=\dfrac{9}{4}\cdot\dfrac{3}{2}=\dfrac{9\cdot3}{4\cdot2}=\dfrac{27}{8}\qquad\text{convert to the mixed number}\\\\=3\dfrac{3}{8}[/tex]
A scientist cools some water at a constant rate. the graph and table show how the temperature of the water changes with time.
CAN SOMEONE ANSWER THIS. ?
Answer:
C
Step-by-step explanation:
The easiest way to determine this is to realize that time is the independent variable (n) and temperature is the dependent variable (a).
From the table, we can plug in the two points (n) into n of each equation and see if that equals the temperature values (a).
A little thinking would get us to plug the numbers in C first.
[tex]a(n)=46-(n-1)*4\\46-(5-1)*4=30[/tex]
Works!!
Now, second number:
[tex]a(n)=46-(n-1)*4\\46-(6-1)*4=26[/tex]
Works!!
Hence, C is the correct answer.
Answer:
[tex]a(n)=46-(n-1) \times 4[/tex]
Step-by-step explanation:
It's important to know that the graph is showing a linear function, which means its equation cannot be exponential. So, choices A and B are not correct here.
To find the correct equation, we could find the slope first with the following formula and the two given points
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\ m=\frac{26-30}{6-5}=4[/tex]
Now, we use the point-slope formula to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-30=4(x-5)\\y=4x-20+30\\y=4x+10[/tex]
Notice that choice C has the same coefficient of 4, which is the slope of the line. Therefore, that's the right answer.
Let's prove it for [tex]n=6[/tex]
[tex]a(n)=46-(n-1) \times 4\\a(6)=46-(6-1) \times 4=46-20=26[/tex]
As the table shows.
Therefore, choice C is correct.
At a competition with 6 runners, medals are awarded for first, second, and
third places. Each of the 3 medals is different. How many ways are there to
award the medals?
Decide if this is a permutation or a combination, and find the number of ways
to award the medals.
Answer: 120 different ways. It is a permutation.
Step-by-step explanation:
Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).
The number of ways to award the medals in 120 different ways.
What is permutation?When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
Given
Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has a first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).
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What is the value of x?
Two intersection lines. Angle formed at the top is labeled 2 x plus 2 degrees. Angle formed at the bottom is labeled 3 x minus 52 degrees.
Answer:
54 is x
Step-by-step explanation:
Sounds like you describing vertical angles. Vertical angles are congruent so that means 2x+2=3x-52
2=1x-52. Subtracted 2x on both sides
54=1x. Added 52 on both sides
54=x. Since 1 times x is x
one hundred fifty-six thousandths in decimals Can u please answer this ASAP I will give you 20 points
Here it is: 0.156
That is the decimal representation of 156/1000
.156.
If they are “thousandths” then you know there is 3 decimal places.
Hope this helps!
An angle measuring pi/8 radians is equal to which of the angle measures given
below? Round your answer to 2 decimal places after each conversion step.
Check all that apply.
A. 22.50
B. 39.25
c. 22°5
D. 22°30
Answer:
A. 22.5° AND D. 22°30’
Step-by-step explanation:
First of all, it's the correct answer on ap*x
To convert π/8 to degrees, replace π with 180°.
π/8 = 180°/8 = 22.5° (A)
Convert 22.5° to degrees minutes seconds
22.5° = 22°30’ (D)
To convert an angle from radians to degrees, multiply by 180/π. The angle measuring π/8 radians is equal to 22.5°.
Explanation:To convert an angle from radians to degrees, we use the conversion factor 180/π. So, an angle of π/8 radians is equal to:
π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°π/8 * 180/π = 22.5°Therefore, the angle measuring π/8 radians is equal to 22.5°.
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NEED URGENT HELP!!!!!!!!)
A bag has 7 blue marbles, 3 red, 2 green, and 8 white. You pick a marble, record its color, and return it. If you repeat this process 150 times, how many times can you expect to pick a blue or red marble? Write your answer as a percent!
Answer:
50%
Step-by-step explanation:
The total number of marbles is 7 + 3 + 2 + 8 = 20
Blue or red means that the total on any one draw is 7 + 3 = 10
You would expect to draw blue or red 1/2 the time.
Out of 150 throws, you would get 1/2 * 150 which is 75 but that is not what you are asked.
% = (1/2 ) * 100 = 50% of the time
Choose the quadratic equation that has a leading coefficient of 1 and solutions 3 and -2.
Options:
A.) x^2+x+6=0
B.) x^2-x-5=0
C.) x^2+x+5=0
D.) x^2-x-6=0
Answer:
Option D [tex]x^{2} -x-6=0[/tex]
Step-by-step explanation:
Verify each quadratic equation
case A) we have
[tex]x^{2} +x+6=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} +(3)+6=0[/tex]
[tex]18=0[/tex] ----> is not true
therefore
x=3 is not a solution of the quadratic equation
case B) we have
[tex]x^{2} -x-5=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} -(3)-5=0[/tex]
[tex]1=0[/tex] ----> is not true
therefore
x=3 is not a solution of the quadratic equation
case C) we have
[tex]x^{2} +x+5=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} +(3)+5=0[/tex]
[tex]17=0[/tex] ----> is not true
therefore
x=3 is not a solution of the quadratic equation
case D) we have
[tex]x^{2} -x-6=0[/tex]
This quadratic equation has a leading coefficient of 1
Substitute the value of x=3 and x=-2 in the equation
For x=3
[tex](3)^{2} -(3)-6=0[/tex]
[tex]0=0[/tex] ----> is true
therefore
x=3 is a solution of the quadratic equation
For x=-2
[tex](-2)^{2} -(-2)-6=0[/tex]
[tex]4+2-6=0[/tex]
[tex]0=0[/tex] ----> is true
therefore
x=-2 is a solution of the quadratic equation
I WILL GIVE BRAINLIEST What is the value of x?
Answer:
A 30
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
100 = 70+x
Subtract 70 from each side
100-70 = 70-70 +x
30 =x
Which of the following shows a number in a fraction form? A. 3/7 B.3 C.1/2 D.3.7
A. and C. are fractions. this is because they are only proportions of a whole unless they are a mixed number. but in this case, these numbers do not go over 1 (a whole).
Answer: Option A and Option C
[tex]\frac{3}{7}[/tex] and [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The numbers in the form of fraction have the following form:
[tex]\frac{b}{c}[/tex]
Where b is known as numerator and c is known as denominator.
To know which of the numbers shown has a fraction form, identify all those with the form [tex]\frac{b}{c}[/tex]
Then you can see that the answer is option A and option C
[tex]\frac{3}{7}[/tex] and [tex]\frac{1}{2}[/tex]
Given the coordinates of the vertices of a pre-image figure, describe how to find the coordinates of the image vertices if the figure is translated vertically.
Step-by-step answer:
Step 1:
find out the amount and direction of the vertical translation.
+3 means translating 3 units up, and -6 means translating 6 units down.
Step 2:
to each of the coordinate pairs, add the value of the translation to the y-coordinate (i.e. the second number of the pair).
For example, if the translation is +3, and if one of the vertices is (4,1), then the image of the vertex is (4,1+3) = (4,4).
Repeat for the rest of the vertices.
Step 3:
Check by graphing both image and preimage to see if the shapes are identical. If not, look for a mistake in the translation process.
To translate a figure vertically, add the translation value to the y-coordinates of each vertex. For a translation of 'k' units, the new vertices will be (x, y + k). This keeps the shape the same and only changes its position vertically.
To find the coordinates of the image vertices when a figure is translated vertically,
you need to follow these simple steps:
Identify the translation value: Determine the distance by which the figure is to be translated vertically. Let's say the translation value is 'k' units.Add the translation value to the y-coordinates: For each vertex of the pre-image figure, a translation involves modifying only the y-coordinate.If the original vertices of the pre-image are (x, y), then the new vertices (image) will be (x, y + k).Suppose you have a triangle with vertices A(2,3), B(5,4), and C(1,7). If the figure is translated vertically by 3 units up, the coordinates of the image vertices will be:This method ensures that the shape of the figure remains unchanged and it is only shifted up or down vertically.
A map has a scale of 3.5 inches = 20 kilometers. If the distance between two cities on the map is 4.9 inches, what is the actual distance between the two cities?
Answer:
28 i think.
Step-by-step explanation:
Answer:
The actual distance between the two cities is 28 kilometers
Step-by-step explanation:
A map has a scale of 3.5 inches = 20 kilometers
Distance between two cities on the map = 4.9 inches
We can use the unitary method in this question to get the actual distance between two cities
∵ 3.5 inches on the map = 20 kilometers
∴ 1 inch distance on the map = [tex]\frac{20}{3.5}[/tex] kilometers
∴ 4.9 inches on the map = [tex]\frac{20}{3.5}\times 4.9[/tex]
= 28 kilometers
Therefore, the actual distance between the two cities is 28 kilometers.
Cot^2 x-csc^2 x=-1 for all values of x. True or false
Answer:
TRUE
Step-by-step explanation:
The well known trigonometry identity states that cot^2(x) + 1 = csc^2(x), rearrangin the equation we have that cot^2(x) - csc^2(x) = -1, which is exactly the expression in the statement. Therefore, the expression is TRUE.
Simplify the expression.
(a^3/2)^3
The simplified expression is [tex]\(\frac{a^9}{8}\)[/tex].
To simplify the expression [tex]\((a^3/2)^3\)[/tex], follow these steps:
1. Apply the power of a power rule, which states that [tex]\((x^m)^n = x^{m \times n}\)[/tex]. In this case, [tex]\(x = a^3/2\)[/tex], [tex]\(m = 1\)[/tex], and [tex]\(n = 3\)[/tex].
2. Distribute the exponent over the numerator and the denominator:
[tex]\((a^3/2)^3 = (a^3)^3 / (2)^3\)[/tex].
3. Apply the power of a power rule to [tex]\((a^3)^3\)[/tex]:
[tex]\((a^3)^3 = a^{3 \times 3} = a^9\)[/tex].
4. Apply the power of a power rule to [tex]\(2^3\)[/tex]:
[tex]\(2^3 = 8\)[/tex].
5. Combine the results to get the simplified expression:
[tex]\(\frac{a^9}{8}\)[/tex].
Therefore, the expression [tex]\((a^3/2)^3\)[/tex] simplifies to [tex]\(\frac{a^9}{8}\)[/tex].
a number multiplied by 1/3 is 1/18
Answer:
1/6
Step-by-step explanation:
[tex]\frac{1}{3}x=\frac{1}{18}\\3(\frac{1}{3}x=\frac{1}{18} )\\[/tex]
[tex]x=3/18\\x=1/6[/tex]
Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period. If x represents the monthly depreciation amount, which expression shows how much Desmond can sell his car for today?
8,000 + 24x
8,000 − 24x
8,000 + 2x
8,000 − 2x
Answer:
8,000-24x
Step-by-step explanation:
there's 24 months in 2 years. If it's value decreased from 8,000 at a constant rate over a 2 year period, the equation would be 8,000-24x
Answer:
B. [tex]8,000-24x[/tex].
Step-by-step explanation:
We have been given that Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period.
Since the value of car depreciates at a constant rate each month, so the value of car depreciated in 2 years would be [tex]2\times 12=24[/tex].
There are 24 months in two years, so value of car depreciated in 2 years would be 24x.
The initial value of car is $8,000, so value of car after 2 years would be [tex]8,000-24x[/tex].
Therefore, option B is the correct choice.
y ≥-1/3 x + 2
y < 2x + 3
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)
Answer:
(2, 2), (3, 1), (4, 2)
Step-by-step explanation:
y ≥-1/3 x + 2
y < 2x + 3
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)
I will assume which we determining which set of points is a solution
(2,2) is in all the sets, so we ignore it
Looking at the graph, we do not have negative solutions for y when x >0 so (3,-1) cannot be a solution and (1,-2) cannot be a solution
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1) x
(2, 2), (1, –2), (0, 2) x
(2, 2), (1, 2), (2, 0)
Again looking at the graph (2,0) is not a solution
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1) x
(2, 2), (1, –2), (0, 2) x
(2, 2), (1, 2), (2, 0) x
Answer:
(2, 2), (3, 1), (4, 2)
Step-by-step explanation:
what is 6 times the quantity x plus 4?
Answer: 6x + 4
6x represents 6 times the quantity x.
+ 4 represents plus 4.
Put 6x and + 4 together to get 6x + 4.
In the problem to the left, if Tim mows 9 lawns this week, by how much will he have exceeded his goal?
Answer:
Step-by-step explanation:
a - number of lawn that Tim needs to mow
310 < 120 + 30a
190 < 30a
6.333 < a
a > 6.333
Tim needs to mow at least 7 lawns to earn more than $310
What is the quotient of 3,968 ÷ 32?
Answer:
124
Step-by-step explanation:
Answer:
124
Step-by-step explanation:
32 goes into 39 one time, 39-32= 7
bring down the 6
32 goes into 76 two times, 76 - 64= 12
bring down the 8
32 goes into 128 four times, 128 - 128 = 0
So 3968/32 = 124
A family membership at a tennis club cost a flat fee of $150, plus $25 per person. If n stands for the number of people, then the membership cost is modeled by ?
Answer:
total cost = 150 + 25n
Step-by-step explanation:
total cost = flat fee + cost per person* number of people
total cost = 150 + 25n
jillian calculates that see will take 95 minutes to run 7 miles. she runs the distance in 80 minutes. what is jillians percent error.
Answer:
15.79%
Step-by-step explanation:
do 95-80 which is 15
then do 15/95 as a fraction then multiply that number by 100 to get 15 15/19 then turn that into a decimal and you get 15.79%
Jillian's percent error in estimating the time it would take her to run 7 miles is 15.79%.
Jillian's percent error in her run can be calculated by taking the absolute value of the difference between her estimated time and actual time, divided by the estimated time, and then multiplied by 100 to get the percentage. Here is the calculation step-by-step:
Calculate the absolute difference between estimated time and actual time: |95 minutes - 80 minutes| = 15 minutes.Divide the difference by the estimated time: 15 minutes / 95 minutes = 0.1579.Multiply by 100 to convert to a percentage: 0.1579 times 100 = 15.79%.Therefore, Jillian's percent error in her estimation is 15.79%.
(-5+1)(((3+6)*2-2)(5)-1) evaluate.
Answer:
-316
Step-by-step explanation:
Each operation shown in bold is done on the next line.
(-5+1)(((3+6)*2-2)(5)-1) =
= (-4)((9*2-2)(5)-1)
= (-4)((18-2)(5)-1)
= (-4)(16(5)-1)
= (-4)(80-1)
= (-4)(79)
= -316
What is the solution to this equation?
x² + 101 = 1
A. 10i, -10i
B. 10,-10
c. -10
D. 10i
Answer:
A. 10i and -10i
Step-by-step explanation:
We are given our equation as
[tex]x^2+101=1\\[/tex]
Let us subtract 101 from both hand sides
[tex]x^2+101-101=1-101\\[/tex]
[tex]x^2=-100[/tex]
Now taking square roots on both hand sides
[tex]\sqrt{x^{2}}} = \sqrt{-100}[/tex]
[tex]x=\sqrt{100} * \sqrt{-1}[/tex]
[tex]x=10 * (+i) \\x=10*(-i)\\[/tex]
[tex]x=+10i \\x=-10i\\[/tex]